What happens if a presidential nominee dies after picking a vice presidential running mate?

Nothing as far as the government is concerned. It's up to the party to promote the v.p. nominee or find a new nominee. If the ballots are printed that's an issue governed by the laws of the individual states. If the states grant the power to the electoral college, then even if the guy AND the V.P. candidate were dead the E.C. would still get the votes and have the power to elect.